4. Find the curvature of r(t) = (tv2, e', e-t) at the point (0,1,1).

Q: 04. Show that the Gauas and mean curvatures on, X-(u+v,u-v, uv) at u=1, v=1 are K=1/16 and H= JI.…

A: Given: 1) X=(u+v,u-v,uv) at u=1,v=1. 2) The paraboloid is xy=aZ.

Q: Find the radius of curvature of a parabola y² - 4x = 0 at the point (4,4). 2

A:

Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A: 2∂z∂x=2xaa=xp, where p=∂z∂x2∂z∂y=2ybb=yq, where q=∂z∂y2z=x2xp+y2yq2z=px+qy

Q: Find the radius of curvature of y=xª at (1,1).

A: Here we have to find the radius of the curvature of y=x4 at (1,1)

Q: Find the radius of curvature at origin at (0,0) y - x = x2 + 2xy + y2

A:

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: What is the curvature of the path of the motion at t=1

A: Since velocity is given we need to calculate  r''(t) only at t=1

Q: 7. Find the radius of curvature of the curve y = In sin x at x= r/2 .

A: the formula used to find the radius of curvature is  K=|y''|1+y'23/2                       (1)R=1K

Q: 3. Find the curvature of the curve given by 7(t) = (t, t², t) nt (-1, 1, –1).

A: Given curve is We know that curvature to given curve at point (-1,1,-1) , that is at t=-1 is

Q: Find the extreme values of the function z= &r+2ry-3r+y+1 and show that only one of the two extrema…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3. Find the curvature of the plane curve (t, t") at t = 1.

A: see below the answer and calculation as per bertleby guideline I have to solve only 1 question. For…

Q: Find the center of curvature of xy = 4 at (2, 2).

A: Solution

Q: Find the curvature of the curve r(t). r(t) = (3 + 6 cos 9t) i - (8 + 6 sin 9t)j + 6k Group of…

A:

Q: Let C(t)=((1/2)cos(t),(1/2)sin(t)) be the circle of radius 1/2 when t is from 0 to 2pi What is the…

A: Given that C(t)=12cost,12sint be the circle of radius 1/2 where t is from 0 to 2π. Here C(t) is a…

Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A: Given equation is 2z=x2a+y2b2p=2xa, where ∂z∂x=p and 2q=2yb, q=∂z∂ya=xp and b=yq2z=x2xp+y2yq2z=px+qy

Q: Evaluate the curvature of ~r(t) = (cosh(t), sinh(t), t)at t = 0

A: we have to evaluate the curvature of r(t)=(cos h(t),sin h(t),t) at t=0

Q: Find the time required by the particle in passing between points which are at distances 4 and 2…

A:

Q: Obtain the curvature of x= k (0 – sin 0); y=k(1+ cos0) in terms of '0'.

A: This is the question from application of advanced Differential Calculus.

Q: 2 - Find the curvature of the curve at the point (1, 0, 0). r(t) (e' cos(t), et sen(t), t) %3D

A:

Q: Find the center of curvature of the curve y =-(e*+e) at (0, 1). (А) (0, 2) в) (1, 1) с) (0, 3) D (0,…

A:

Q: Find the curvature of ƒ(x) = ln cos x, < x < 2 -- 2°

A:

Q: Let C be the curve represented by Ŕ(t) = (cos 2t, 2√3t, 5 — sin 2t). - ㅠ Determine the curvature of…

A: To find out the curvature of C.

Q: Let the the position vecor be R(t) = (-t,2 cos(2t),2 sin(2t)). Compute the curvature x(t).

A: The position vector Rt=-t,2cos2t,2sin2t. We have curvature k(t).

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Find the…

A:

Q: Find the curvature of r(t) = (2 cos(t), sin(t), 3) at t = = 1.

A:

Q: Compute the mean curvature of the surface z = xy at the origin

A:

Q: Find the curvature K(t) of the curve r(t) = (2 sin t, 2, 2 cos t) when t = T/ 4 1 2 O 1 8 1 8 4 O 2

A:

Q: Find the center of curvature of y = x3 at the point (1, 1) A. (-4, 8/3) C. (6, -2/3) B. (4, -8/3)…

A:

Q: What is the radius of curvature at point (1, 2) of the curve 4x – y2 = 0.

A:

Q: At what point does the curve y = e have maximum curvature? What happens to the curvature as x → ∞?

A:

Q: 4. Given that r(t) = cos ti + sin tj + In cos tk Find the curvature k and vec- tors T, N, B at the…

A: Find curvature at t=1

Q: The curvature of the curve 7 (t)={2t, 2t+1, sin2t) at t= is 4 O 1 O 1 O 2 1/818 1/2

A: Here the given curve is r(t)⇀ ==(2t,2t+1,sin2t) Here we have to find the curvature of the curve at…

Q: Find the curvature of the curve F(t) = (cos(5t), sin(5t), 3t) at the point t

A:

Q: Find the curvature of r(t) = at the point (1,0,0)

A:

Q: Find the y coordinate of the center of curvature of th parabola at (2,2).

A:

Q: Find the center of curvature of the curve y=Inx at (1, 0). A) (4, 3) (в) (3,4) c) (3, -2) D (-2, 3)

A: Ans D

Q: 15. y= 2x +3 at x = 27

A:

Q: The curvature of the curve 7 (t)= (2t, 2t+ 1, sin2t) at t= TT is 4. 1 18 O 1 1/8 1/2 O O O O

A: The given curve is r(t)→=2t,2t+1,sin(2t) We know that the curvature κ(t) for r(t)→ is given by the…

Q: 6. Consider the same curve from the last problem, C parametrized by T(t) = (2 cos t, –1,2 sin t)…

A:

Q: Find the curvature of y = sin(-lx) at x = .

A: Solution:-

Q: 1) Calculate the curvature of the position vector F(t) = sin t ax + 2cost ay + V3 sin t āz is a…

A: Formula of Curvature(K) of the position vector r(t):…

Q: 8. Find the curvature of the vector-valued function r(t) = at the point t = -1.

A: given function is rt=3t2,-4t,1t find the curvature at t=-1 k=r→'t×r→''tr→'t3

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = x3, x = 2

A: Consider the following equation of curve: y=x3 Differentiate y with respect to x: dydx=ddxx3y'=3x2…

Q: 5. Find the Curvature of ř (t) = L", Int,tInt) at the point (1,0.0)

A:

Q: Show that if M" has constant sectional curvature C then Ricci and scalar curvature of M" are Ric =…

A: We know that from given data: If M has a constant sectional curvature C , k. The Uniqueness of this…

Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A:

Q: 5. Find the curvature of the cardioid r= 3( 1+ cos 0 ) at 0= T.

A: Formula: curvature=r2+2r'2-rr''r2+r'232

Q: Show that the Gauas and mean curvatures on , X = (u + v,u –- v,uv) at u = 1, v = 1 are K = 116 and H…

A: Given, X=u+v,u-v,uv u=1,v=1 , k=116 and H=182 We know that, E=xu,xuF=xu,xvG=xv,xv So, we need to…

Q: x= 0, x= π &x= π

A:

Q: At what point does the curve have maximum curvature? y = 7 In(x) (x, y) = What happens to the…

A: Given,              y = 7 ln(x)